Nuclear magnetic resonance (NMR) can be used to determine properties of a substance. Oil and gas field tools use NMR systems to investigate the properties of earth formations, such as the porosity of formations or the composition of fluids within the formations. In one example, the NMR system is lowered into a wellbore that traverses a formation. The NMR system can be lowered into the wellbore as part of a wireline or drilling string. The NMR system is used to investigate the properties of the formation adjacent to the wellbore. The system includes a magnet for applying a static magnetic field to the formation adjacent to the wellbore. The system also includes a coil for applying an oscillating magnetic field to the formation adjacent to the wellbore. The oscillating field is composed of a sequence of pulses that tip the magnetization of the atomic nuclei within the formation away from an initial magnetization produced by the magnet. The sequence of pulses and the static magnetic field interact with the nuclei in a manner such that a NMR signal composed of “echoes” is generated within at least a portion of the formation. The NMR signal within the formation is detected using the coil and used to determine the properties for the formation.
Due to the weak magnetic field produced by the magnet and the limited sensitivity of the coil, the depth of investigation of such wellbore NMR systems is limited. For example, in some cases, the depth of investigation is between 2 and 10 cm. Also, the static field applied to the formation is inhomogeneous because the field decreases in strength as a function of distance from the magnet. Because of this inhomogeneous field, the NMR signal is produced in a small portion of the formation. This small portion is known as a “shell.” In some cases, the shell has a volume of 10−4 m3 (100 cc). Accordingly, to investigate a large area, the NMR system determines the properties of multiple shells. Investigating multiple shells is time consuming and is a particular problem in wireline or drilling applications where time is costly.